Superconducting field-programmable gate array

ABSTRACT

The various embodiments described herein include methods, devices, and systems for operating superconducting circuitry. In one aspect, a programmable circuit includes: (1) a superconducting component arranged in a multi-dimensional array of alternating narrow and wide portions, the superconducting component having an input terminal at a first end and an output terminal at a second end opposite of the first end; and (2) control circuitry coupled to the narrow portions of the superconducting component, the control circuitry configured to transition the narrow portions between superconducting and non-superconducting states.

RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 62/751,601, filed Oct. 27, 2018, entitled “SuperconductingField-Programmable Gate Array,” which is hereby incorporated byreference in its entirety.

This application is related to U.S. patent application Ser. No.16/107,143, filed Aug. 21, 2018, entitled “Superconductor-to-InsulatorDevices,” U.S. patent application Ser. No. 16/136,124, filed Sep. 19,2018, entitled “Methods and Devices for Impedance Multiplication,” andU.S. Provisional Application No. 62/660,192, filed Apr. 19, 2018,entitled “Superconducting Field-Programmable Gate Array,” each of whichis hereby incorporated by reference in its entirety.

TECHNICAL FIELD

The circuits and circuit components described in this document relategenerally to reconfigurable superconducting components, including butnot limited to, reconfigurable superconducting field-programmable gatearrays (FPGAs).

BACKGROUND

Analog circuits are used to implement various functions and performoperations on one or more inputs to produce an output. Thus, analogcircuits are essential components in many electronic devices.Field-programmable gate arrays (FPGAs) are circuits designed to beconfigurable by a user after manufacturing. FPGAs generally includemultiple circuit elements with reconfigurable interconnects that enablethe elements to be wired in different configurations to perform morecomplex combinational functions.

Superconductors are materials capable of operating in a superconductingstate with zero electrical resistance under particular conditions.

SUMMARY

There is a need for systems and/or devices with more efficient andeffective methods for implementing programmable operations. Suchsystems, devices, and methods optionally complement or replaceconventional systems, devices, and methods for implementing programmableoperations.

Utilizing superconductor(s) to implement analog circuit(s) allows thecircuit(s) to operate at cryogenic temperatures and at nanoscale sizes,or from a different perspective, implementing such circuits utilizingsuperconductors or one or more superconductor elements allows suchcircuits to benefit from the properties of superconductors. For example,such devices would be beneficial for low-latency operations directly ona cryogenic chip.

Accordingly, some embodiments include a device with multiplesuperconducting wires (e.g., superconducting thin-film nanowires) makinga circuit, where each nanowire is thermally-coupled to a gate input. Insome embodiments, the gate inputs are optionally configured to operatein a steady state, e.g., constantly maintaining the correspondingnanowire in a superconducting state or constantly maintaining thecorresponding nanowire in a non-superconducting state. The steady stateinputs enable different configurations of the superconducting nanowires,thereby adjusting capacitance, inductance, and resistance of thecircuit.

In some embodiments, the gate inputs are heat sources that arethermally-coupled to, and electrically insulated from, the respectivesuperconducting wires. In these embodiments, the heat sources areconfigured to selectively provide heat sufficient to selectivelytransition the corresponding superconducting wires from thesuperconducting state to the non-superconducting (e.g., conductive)state. In some embodiments, the gate inputs can include strain-inducingelements, such as piezoelectrics and the like, that arephysically-coupled to the respective superconducting wires. In theseembodiments, the strain-inducing elements can be configured toselectively provide a strain (stress) on the correspondingsuperconducting wires sufficient to selectively transition those wiresfrom the superconducting state to an insulating state.

In one aspect, some embodiments include a programmable circuit having:(1) a superconducting component arranged in a multi-dimensional array ofalternating narrow and wide portions, the superconducting componenthaving an input terminal at a first end and an output terminal at asecond end opposite of the first end; and (2) control circuitry coupledto the narrow portions of the superconducting component, the controlcircuitry configured to selectively transition the narrow portionsbetween superconducting and non-superconducting states. In someembodiments, the superconducting component is a thin film ofsuperconducting material. In some embodiments, the superconductingcomponent consists essentially of a thin film of superconductingmaterial. In some embodiments, the superconducting component isconfigured such that in response a gate input from the control circuitrythe corresponding narrow portion transitions from a superconductingstate to a non-superconducting state.

In another aspect, some embodiments include a programmable circuit,having: (1) a configurable superconducting component having an inputterminal, an output terminal, and a plurality of gate terminals; and (2)control circuitry coupled to the superconducting component via theplurality of gate terminals, the control circuitry adapted toselectively adjust capacitance, inductance, and/or resistance of thesuperconducting component.

In another aspect, some embodiments include a method of operating aprogrammable circuit. The method includes: (1) providing a first currentto a superconducting component arranged in a multi-dimensional array ofalternating narrow and wide portions, the first current configured tomaintain the superconducting component in a superconducting state; (2)configuring the superconducting component to perform a first operationby providing constant heat (or piezoelectric strain) to a first subsetof the narrow portions, the constant heat configured to transition thefirst subset of narrow portions from the superconducting state to anon-superconducting state; (3) while the superconducting component isconfigured to perform the first operation: (a) receiving one or moreinputs via a second subset of the narrow portions, distinct from thefirst subset; and (b) obtaining an electrical output via a subset of thewide portions, the electrical output corresponding to a result of thefirst operation on the one or more inputs.

Thus, superconducting devices and systems are provided with methods forprogramming and operating circuitry, thereby increasing theeffectiveness, efficiency, and user satisfaction with such circuitry.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the various described embodiments,reference should be made to the Detailed Description below, inconjunction with the following drawings in which like reference numeralsrefer to corresponding parts throughout the figures.

FIGS. 1A-1B are schematic diagrams illustrating representativesuperconducting arrays in accordance with some embodiments.

FIG. 2 is a schematic diagram illustrating a representativesuperconducting circuit in accordance with some embodiments.

FIG. 3 is a schematic diagram illustrating another representativesuperconducting circuit in accordance with some embodiments.

FIGS. 4A-4B are schematic diagrams illustrating a representativesuperconducting circuit in an example programmed state in accordancewith some embodiments.

FIGS. 5A-5B are schematic diagrams illustrating a representativesuperconducting circuit in another example programmed state inaccordance with some embodiments.

FIG. 6A is a schematic diagram illustrating a representativesuperconducting circuit in another example programmed state inaccordance with some embodiments.

FIGS. 6B-6F are prophetic diagrams illustrating a representativeoperating sequence of the superconducting circuit of FIG. 6A inaccordance with some embodiments.

FIG. 7 is a schematic diagram illustrating a representativesuperconducting circuit in accordance with some embodiments.

FIG. 8A is a schematic diagram illustrating a representativesuperconducting circuit in an example programmed state in accordancewith some embodiments.

FIGS. 8B-8D are diagrams illustrating representative operating states ofthe superconducting circuit of FIG. 8A in accordance with someembodiments.

FIGS. 8E-8F are prophetic diagrams illustrating relationships betweengate signals and capacitance of the superconducting circuit of FIG. 8Ain accordance with some embodiments.

FIGS. 9A-9B are schematic diagrams illustrating a representativesuperconducting circuit in an example programmed state in accordancewith some embodiments.

FIG. 10A is a schematic diagram illustrating a representativesuperconducting circuit in an example programmed state in accordancewith some embodiments.

FIGS. 10B-10F are prophetic diagrams illustrating representativeoperating states of the superconducting circuit of FIG. 10A inaccordance with some embodiments.

FIGS. 10G-10H are prophetic diagrams illustrating relationships betweengate signals and resistance of the superconducting circuit of FIG. 10Ain accordance with some embodiments.

DETAILED DESCRIPTION

Reference will now be made in detail to embodiments, examples of whichare illustrated in the accompanying drawings. In the following detaileddescription, numerous specific details are set forth in order to providea thorough understanding of the various described embodiments. However,it will be apparent to one of ordinary skill in the art that the variousdescribed embodiments may be practiced without these specific details.In other instances, well-known methods, procedures, components,circuits, and networks have not been described in detail so as not tounnecessarily obscure aspects of the embodiments.

Many modifications and variations of this disclosure can be made withoutdeparting from its spirit and scope, as will be apparent to thoseskilled in the art. The specific embodiments described herein areoffered by way of example only, and the disclosure is to be limited onlyby the terms of the appended claims, along with the full scope ofequivalents to which such claims are entitled.

As used herein, a “superconducting circuit” or “superconductor circuit”is a circuit having one or more superconducting materials. For example,a superconducting logic circuit is a logic circuit that includes one ormore superconducting materials. As used herein, a “superconducting”material is a material that is capable of operating in a superconductingstate (under particular conditions). For example, a material thatoperates as a superconductor (e.g., operates with zero electricalresistance) when cooled below a particular temperature (e.g., a criticaltemperature) and having less than a maximum current flowing through it.The superconducting materials may also operate in an “off” state wherelittle or no current is present. In some embodiments, thesuperconducting materials operate in a non-superconducting state duringwhich the materials have a non-zero electrical resistance (e.g., aresistance in the range of one thousand to ten thousand ohms). Forexample, a superconducting material supplied with a current greater thana threshold superconducting current for the superconducting material maytransition from a superconducting state with zero electrical resistanceto a non-superconducting state with non-zero electrical resistance. Asan example, superconducting thin film 122 is a superconducting materialthat is capable of operating in a superconducting state (e.g., underparticular operating conditions).

As used herein, a “wire” is a section of material configured fortransferring electrical current. In some embodiments, a wire includes asection of material conditionally capable of transferring electricalcurrent (e.g., a wire made of a superconducting material that is capableof transferring electrical current while the wire is maintained at atemperature below a threshold temperature). A cross-section of a wire(e.g., a cross-section that is perpendicular to a length of the wire)optionally has a geometric (e.g., flat or round) shape or an irregular(also sometimes called a non-geometric) shape. In some embodiments, alength of a wire is greater than a width or a thickness of the wire(e.g., the length of a wire is at least 5, 6, 7, 8, 9, or 10 timesgreater than the width and the thickness of the wire).

FIGS. 1A-1B are schematic diagrams illustrating representativesuperconducting arrays in accordance with some embodiments. FIG. 1A is aschematic diagram illustrating a superconducting array 120 in accordancewith some embodiments. The superconducting array 120 includesalternating wide portions 124 and narrow portions 126, 128. In someembodiments, the narrow portions 126, 128 each have a width that is lessthan a width of a wide portion 124 (e.g., half or a quarter of the widthof a wide portion 124). In some embodiments, each wide portion 124 has asame length and/or width as other wide portions 124. In someembodiments, each narrow portion 126, 128 has a same length and/or widthas other narrow portions 126, 128. In some embodiments, a first subsetof the narrow portion 126, 128 have a different length and/or width as asecond subset of the narrow portions 126, 128. For example, in someembodiments, the narrow portions 128 have a different width than thenarrow portions 126. In some embodiments, the narrow portions 126, 128each have a width ranging from 50 nanometers (nm) to 5 microns (μm). Insome embodiments, the narrow portions 126, 128 each have a lengthranging from 200 nm to 2 microns μm. In some embodiments, the wideportions 124 each have a width ranging from 100 nm to 10 μm. In someembodiments, the wide portions 124 each have a length ranging from 100nm to 10 microns μm. In accordance with some embodiments, thesuperconducting array 120 includes ‘n’ columns and ‘p’ rows, where ‘n’and ‘p’ range from 1 to many (e.g., 10, 50, or 100). In someembodiments, each row of the superconducting array 120 has a same numberof columns as other rows (e.g., the superconducting array 120 isrectangular in shape). In some embodiments, a first subset of the rowsof the superconducting array 120 has a different number of columns as asecond subset of the rows. In some embodiments, a first subset of thecolumns of the superconducting array 120 has a different number of rowsas a second subset of the columns.

In some embodiments, the thin film 122 includes a thin film of one ormore superconducting materials, such as niobium or niobium alloys. Inaccordance with some embodiments, each wide portion of thesuperconducting component 100 has a corresponding terminal.Alternatively, in some embodiments, less than all of wide portions ofthe superconducting component have corresponding terminals to whichother circuitry or components can be electrically coupled.

Although some of the Figures show examples of superconductors havingrectangular geometry, in some embodiments, the various superconductorsdescribed herein have other geometric (e.g., oval or circular) ornon-geometric forms. FIG. 1B illustrates a superconducting array 130 inaccordance with some embodiments. The superconducting array 130 iscomposed of a superconducting thin film 131 having alternating wideportions 132 and narrow portions 134, 136 defined by curved (oval)cutouts 138 in accordance with some embodiments. In some embodiments,the various circuits described herein utilize a thin film with curvededges, such as those of the thin film 131. Curved edges and roundedcorners improve current flow in some circumstances by reducing currentcrowding at corners. Curved edges, such as those in FIG. 1B, also reducecapacitive coupling between wide portions 132 (e.g., reduce cross-talk)in some circumstances as compared to straight edges.

FIG. 2 is a schematic diagram illustrating a superconducting circuit 200in accordance with some embodiments. The superconducting circuit 200includes a thin film 201 having alternating narrow and wide portions.The superconducting circuit 200 also includes a heat source 202thermally coupled to each narrow portion (e.g., the heat source is on alayer above or below the layer of the thin film 201), or to a subset ofthe narrow portions. In some embodiments, one or more of the narrowportions is not thermally coupled to a heat source 202. For example, thesuperconducting circuit 200 is configured such that one or more of thenarrow portions is to be maintained in a superconducting state, andaccordingly a heat source 202 is not coupled to those portions. In someembodiments, a heat source 202 is thermally-coupled andelectrically-isolated from a corresponding narrow portion, e.g., toprevent current flow and quantum tunneling. In some embodiments, theheat sources 202 include two or more types of heat sources, e.g., afirst type of heat source comprising a photon detection circuit and asecond type of heat source comprising a resistor.

In some embodiments, rather than a heat source 202, a piezoelectricsource is coupled to each narrow portion, or a subset of the narrowportions. In some embodiments, each piezoelectric source is physicallycoupled to a corresponding narrow portion and configured to selectivelyapply a strain (stress) on the narrow portion. In some embodiments, thestrain applied to the narrow portion is sufficient to transition thenarrow portion from the superconducting state to an insulating (highresistance) state. Although the following figures are shown anddescribed with heat sources, one of skill in the art, after reading thepresent disclosure would recognize that the individual heat sourcescould be replaced with piezoelectric sources.

The superconducting circuit 200 also includes a plurality of electricalterminals 204 on the plurality of wide portions, the terminals 204configured to be coupled to a respective input and/or output component(e.g., a readout circuit, an electrical ground, or a current source). Insome embodiments, one or more of the wide portions of thin film 201 isnot connected to a respective terminal 204. In some embodiments, theterminals 204 are connected to the wide portions at positions other thanthose shown in FIG. 2. In some embodiments, the terminals 204 includetwo or more types of terminals, e.g., composed of different materialsand/or having varying dimensions, resistances, and/or impedances. Asdiscussed below, the superconducting circuit 200 is programmable byadjusting operation of the heat sources 202.

FIG. 3 is a schematic diagram illustrating a superconducting circuit 300in accordance with some embodiments. FIG. 3 shows the top terminals ofthe thin film 201 (e.g., terminals 204-1-204-6, FIG. 2) coupled to oneanother and having a shared terminal 304. The terminal 304 is coupled toa current source 308. In some embodiments, the current source 308 isconfigured to supply a bias current to the thin film 201 so that thethin film 201 operates in a superconducting state in the absence ofother inputs (e.g., in the absence of heat from the heat sources 202).FIG. 3 further shows the bottom terminals of the thin film 201 (e.g.,terminals 204-9-204-14, FIG. 2) coupled to one another and having ashared terminal 302. The terminal 302 is coupled to a readout circuit306. In some embodiments, the readout circuit 306 is configured todetermine, or react to, a current, resistance, inductance, orcapacitance value of the thin film 201.

FIGS. 4A-4B are schematic diagrams illustrating a superconductingcircuit 400 in an example programmed state (e.g., a selective capacitor)in accordance with some embodiments. The superconducting circuit 400 inFIG. 4A includes the superconducting circuit 300 of FIG. 3 and a gateline coupled to heat sources 202-2, 202-3, 202-9, 202-8, 202-11, 202-14,202-17, 202-19, 202-21, 202-24, and 202-27. In some embodiments, thegate line is a conductive path or wire, e.g., on a same layer as theheat sources, or electrically coupled to the heat sources through acontact or via. In some embodiments, the gate line is composed ofsuperconducting materials. In some embodiments, the gate line is a madeof metal or a semiconductor. In some embodiments, the gate line operatesin a superconducting state, while in other embodiments, the gate lineoperates in a non-superconducting, conductive state. In accordance withsome embodiments, activation of the gate line causes the heat sources togenerate heat sufficient to transition the corresponding narrow portionsof the thin film 201 from the superconducting state to anon-superconducting (e.g., conductive) state. In some embodiments, theheat sources 202 shown in FIG. 3 and not shown in FIG. 4A are disabledin the example programmed state, e.g., the omitted heat sources areelectrically-grounded or disconnected from any source so as not toprovide any heat to the corresponding narrow portions.

Although FIG. 4A shows the heat sources coupled together via the gateline, in some embodiments, the heat sources are independently controlledand/or operated. In some embodiments, the heat sources 202-2, 202-3,202-9, 202-8, 202-11, 202-14, 202-17, 202-19, 202-21, 202-24, and 202-27are individually programmed to operate concurrently (e.g., in unison).

FIG. 4B shows the thin film 201 with the narrow portions in thenon-superconducting state removed. As shown in FIG. 4B, activation ofthe gate line creates an open circuit with charge build-up between thecurrent source 308 and the readout circuit 306. Thus, in theconfiguration shown in FIGS. 4A-4B the superconducting circuit 400selectively operates as a capacitor (e.g., with a capacitance in thefemtofarad (fF) to picofarad (pF) range).

FIGS. 5A-5B are schematic diagrams illustrating a superconductingcircuit 500 in another example programmed state (e.g., a selectivecapacitor) in accordance with some embodiments. The superconductingcircuit 500 in FIG. 5A is similar to the superconducting circuit 400 inFIG. 4A, except that the gate line is coupled to a greater number ofheat sources (e.g., heat sources 530-1 through 503-33 arranged in anoscillating comb-tooth pattern) than the superconducting circuit 400 inFIG. 4B. Similar to FIG. 4A, terminal 504 is coupled to a current source308 and terminal 502 is coupled to readout circuit 510. The greaternumber of heat sources in use in FIGS. 5A-5B result in greatercapacitance than the circuit in FIGS. 4A-4B. In accordance with someembodiments, activation of the gate line causes the heat sources togenerate heat sufficient to transition the corresponding narrow portionsof the thin film 502 from the superconducting state to anon-superconducting (e.g., conductive) state. FIG. 5B shows the thinfilm 502 with the narrow portions in the non-superconducting stateremoved. Activation of the gate line creates an open circuit with chargebuild-up between the current source 308 and the readout circuit 510.Thus, in the configuration shown in FIGS. 5A-5B the superconductingcircuit 500 selectively operates as a capacitor, with a differentcapacitance than the configuration shown in FIGS. 4A-4B. Therefore,adjusting the number and arrangement of heat sources that are coupled tothe gate line allows for adjustment of the resulting capacitance of thecircuit.

Although FIG. 5A shows the heat sources coupled together via the gateline, in some embodiments, the heat sources are independently controlledand/or operated. In some embodiments, the heat sources are individuallyprogrammed to operate concurrently (e.g., using control circuitrycoupled to the heat sources).

FIG. 6A is a schematic diagram illustrating a superconducting circuit600 in another example programmed state (e.g., a current amplifier) inaccordance with some embodiments. FIG. 6A shows the superconductingcircuit 600 including the superconducting circuit 200 (FIG. 2) with thetop terminals of the thin film 201 (e.g., terminals 204-1-204-6, FIG. 2)coupled to one another and having a shared terminal 603. The terminal603 is coupled to a current source 607. The top terminals of the thinfilm 201 are further coupled to a readout circuit 608 via a resistor606. In some embodiments, the current source 607 is configured to supplya bias current to the thin film 201 so that the thin film 201 operatesin a superconducting state in the absence of other inputs (e.g., in theabsence of heat from the heat sources 202). FIG. 6A further shows thebottom terminals of the thin film 201 (e.g., terminals 204-9-204-14,FIG. 2) coupled to one another and having a shared terminal 605. Theterminal 605 is coupled to a reference node 602 (e.g., an electricalground).

FIG. 6A further shows a gate line coupled to the heat source 202-2 in afirst column of the thin film 201, and a bias line coupled to the heatsources 202-7, 202-11, 202-16, 202-21, and 202-26 in the remainingcolumns of the thin film 201. The bias line includes resistors (e.g.,resistors 610, 612, 614, 616, and 618) coupled to the respective heatsources. In accordance with some embodiments, the resistor 612 has ahigher resistance value than the resistor 610, the resistor 614 has ahigher resistance value than the resistor 612, the resistor 616 has ahigher resistance value than the resistor 614, and the resistor 618 hasa higher resistance value than the resistor 618. In accordance with someembodiments, the bias line is coupled to a bias source and the biassource is configured to provide a current to the heat sources 202. Thecurrent from the bias source is split between the heat sources inaccordance with the resistances of the resistors 610-618. In accordancewith some embodiments, each heat source 202 generates heat proportionalto the amount of current received by the heat source. Accordingly,biased as shown, heat sources 202-7, 202-11, 202-16, 202-21, and 202-26provide heat to their respective narrow portions with the heat appliedto each narrow portion decreasing from left to right. In accordance withsome embodiments, the generated heat at each narrow portion isinsufficient to transition that respective narrow portions from thesuperconducting state to a non-superconducting state, but the heatapplied does result in the narrow portion corresponding to heater 202-7being biased closer to its threshold current than the narrow portioncorresponding to heater 202-26. That is, the generated heat adjusts thecorresponding narrow portions to be closer to, but not exceeding, eachnarrow portion's superconducting current threshold with the differencebetween the narrow portions bias current and threshold currentincreasing from left to right in the figure. As described in furtherdetail below, such a sequential biasing provides for the individualcolumns of the array to switch to a normal state in a sequential fashion(i.e., the system can operate as a cascading superconducting nanowireamplifier) when a gate current is applied to the gate heater 202-6.Advantageously, such an arrangement does not require different columnsinductances to trigger the cascade and is therefore faster and possessesa higher dynamic range than embodiments that employ columns havingdifferent inductors (e.g., by requiring that the columns to havesequentially increasing lengths). While FIGS. 6A-6F show a gate arrayhaving 5 columns and two rows of heaters/narrow portions any number ofcolumns can be used in combination with one or more narrow portionswithout departing from the scope of the present disclosure.

Although FIG. 6A shows the heat sources coupled together via the biasline, in some embodiments, the heat sources are independently controlledand/or operated. In some embodiments, the heat sources 202-7, 202-11,202-16, 202-21, and 202-26 are individually programmed to operateconcurrently. For example, each heat source is coupled to a distinctcurrent source configured to supply a same current as results from thecurrent divider shown in FIG. 6A.

FIGS. 6B-6F are prophetic diagrams illustrating a representativeoperating sequence of the superconducting circuit 600 of FIG. 6A inaccordance with some embodiments. FIG. 6B shows a bias current 619received at the bias line and distributed to the heat sources 202-7,202-11, 202-16, 202-21, and 202-26. FIG. 6B also shows a current 620from the bias current source 607. The current 620 distributes throughthe thin film 201 with a portion flowing through each column of the thinfilm, e.g., current portion 622 flowing through the first column,current portion 624 flowing through the second column, current portion626 flowing through the third column, current portion 628 flowingthrough the fourth column, current portion 630 flowing through the fifthcolumn, and current portion 632 flowing through the sixth column. FIG.6B further shows the current 621 flowing from the thin film 201 to thereference node 602. In accordance with some embodiments, the current 621is equal to the current 620 because the thin film 201 has zeroelectrical resistance and thus no current flows through the resistor 606to the readout circuit 608.

FIG. 6C shows an input current 640 received at the gate line at a firsttime. The current 640 causes the heat source 202-2 to generate heat andthe generated heat causes the corresponding narrow portion 648 totransition from the superconducting state to a non-superconductingstate. Once the narrow portion 648 transitions to thenon-superconducting state, the current previously flowing through thenarrow portion 648 redirects to the other columns of the thin film 201.FIG. 6D shows the narrow portion 650 corresponding to heat source 202-7transitioning to the non-superconducting state at a second time, inresponse to receiving the redirected current. In accordance with someembodiments, the heat generated by the heat source 202-7 lowers thesuperconducting current threshold for the narrow portion 650 and theredirected current exceeds the lowered superconducting current thresholdof the narrow portion 650. Therefore, the narrow portion 650 transitionsfrom the superconducting state to the non-superconducting state. Oncethe narrow portion 650 transitions to the non-superconducting state, thecurrent previously flowing through the narrow portion 650 redirects tothe other columns of the thin film 201 that are still in thesuperconducting state.

FIG. 6E shows the narrow portion 652 corresponding to heat source 202-11transitioning to the non-superconducting state at a third time, inresponse to receiving the redirected current. In accordance with someembodiments, the heat generated by the heat source 202-11 lowers thesuperconducting current threshold for the narrow portion 652 (though notas much as the heat from heat source 202-7 lowers the threshold for thenarrow portion 650) and the redirected current exceeds the loweredsuperconducting current threshold of the narrow portion 652. Therefore,the narrow portion 652 transitions from the superconducting state to thenon-superconducting state. Once the narrow portion 652 transitions tothe non-superconducting state, the current previously flowing throughthe narrow portion 652 redirects to the other columns of the thin film201 that are still in the superconducting state. In a similar manner,the narrow portions 654, 656, and 658 sequentially transition from thesuperconducting state to a non-superconducting.

FIG. 6F shows each narrow portion 648-658 in the non-superconductingstate and current from the current source 607 redirected to the readoutcircuit 608 via the resistor 606. In some embodiments, the resistor 606is configured to have a resistance value significantly less thanrespective resistances of the narrow portions while the narrow portionsare in the non-superconducting state (e.g., 1/10, 1/100, or 1/1000 theresistance of the individual narrow portions). Thus, FIGS. 6B-6F show asequential transition of the narrow portions of the thin film 201 inresponse to a current received at the gate line. FIGS. 6B-6F furthershow current from the bias current source 607 provided to the readoutcircuit 608 (via the resistor 606) after transition of the narrowportions. In accordance with some embodiments, the current 620 from thecurrent source 607 is significantly larger than the current 640 suppliedto the gate line (e.g., 10 times or 100 times as much current). In thisway, a relatively small input gate current results in a relativelylarger current being supplied to the readout circuit 608.

FIG. 7 is a schematic diagram illustrating a superconducting circuit 700in accordance with some embodiments. The superconducting circuit 700 issimilar to the superconducting circuit 300 in FIG. 3, except that thethin film 702 in FIG. 7 has more rows and columns than the thin film 201in FIG. 3. Similar to FIG. 3, terminal 704 is coupled to a currentsource 308 and terminal 706 is coupled to readout circuit 710. Althoughnot shown in FIG. 7, each narrow portion of the thin film 702 is coupledto a source (e.g., a heat source or piezoelectric source).

FIG. 8A is a schematic diagram illustrating a superconducting circuit800 in an example programmed state (e.g., variable capacitor) inaccordance with some embodiments. The superconducting circuit 800includes the superconducting circuit 700 of FIG. 7 and a gate linecoupled to three sets of heat sources, each set spanning the width ofthe thin film 702 (e.g., each set similar to the configuration shown inFIG. 4A and described above). The gate line in FIG. 8A is coupled toeach set of heat sources via a resistor. In some embodiments, theresistors 810, 812, and 814 have different respective resistance values(e.g., the resistors operate as a current divider for current providedto the gate line). For example, in accordance with some embodiments, theresistor 812 has a higher resistance value than the resistor 810, andthe resistor 814 has a higher resistance value than the resistor 812.Although FIG. 8A shows the heat sources coupled together via the gateline, in some embodiments, the heat sources are independently controlledand/or operated (e.g., are individually programmed to operateconcurrently with other heat sources in the same set).

FIGS. 8B-8D are diagrams illustrating representative operating states ofthe superconducting circuit of FIG. 8A in accordance with someembodiments. FIG. 8B shows a first current, current 850, received at thegate line. FIG. 8B further shows the first set of heat sources 805supplying sufficient heat to the corresponding set of narrow portions(e.g., narrow portion 803) to transition the narrow portions from thesuperconducting state to the non-superconducting state. The transitionof the first set of narrow portions results in a first capacitancebetween the current source 308 and the readout circuit 710 ofsuperconducting circuit 800.

FIG. 8C shows a second current, current 852 (e.g., greater than thecurrent 850 in FIG. 8B), received at the gate line. FIG. 8C also showsthe first set of heat sources 805 supplying sufficient heat to thecorresponding set of narrow portions (e.g., narrow portion 803) totransition the narrow portions from the superconducting state to thenon-superconducting state. FIG. 8C further shows the second set of heatsources 809 supplying sufficient heat to the corresponding set of narrowportions (e.g., narrow portion 807) to transition the narrow portionsfrom the superconducting state to the non-superconducting state. Thetransition of the first set of narrow portions and the second set ofnarrow portions results in a second capacitance (e.g., less capacitancethan the first capacitance of FIG. 8B) between the current source 308and the readout circuit 710 of superconducting circuit 800.

FIG. 8D shows a third current, current 854 (e.g., greater than thecurrent 852 in FIG. 8C), received at the gate line. FIG. 8D also showsthe first set of heat sources 805 supplying sufficient heat to thecorresponding set of narrow portions (e.g., narrow portion 803) totransition the narrow portions from the superconducting state to thenon-superconducting state. FIG. 8D further shows the second set of heatsources 809 supplying sufficient heat to the corresponding set of narrowportions (e.g., narrow portion 807) to transition the narrow portionsfrom the superconducting state to the non-superconducting state. FIG. 8Dfurther shows the second set of heat sources 813 supplying sufficientheat to the corresponding set of narrow portions (e.g., narrow portion811) to transition the narrow portions from the superconducting state tothe non-superconducting state. The transition of the first set of narrowportions, the second set of narrow portions, and the third set of narrowportions results in a third capacitance (e.g., less capacitance than thesecond capacitance of FIG. 8C) between the current source 308 and thereadout circuit 710.

FIGS. 8E-8F are prophetic diagrams illustrating relationships betweengate current 870 and capacitance of the superconducting circuit of FIG.8A in accordance with some embodiments. FIG. 8E shows a gate current 870changing over time. Specifically, the gate current 870 transitions frombelow the Threshold 1 to above the Threshold 1 at a first time t₁. Anexample of a current that is between the Threshold 1 and the Threshold 2is the current 850 in FIG. 8B. As shown in FIG. 8F, a current betweenthe Threshold 1 and the Threshold 2 corresponds to a capacitance 866,e.g., due to the first set of narrow portions transitioning to thenon-superconducting state as shown in FIG. 8B. The gate current 870transitions from below the Threshold 2 to above the Threshold 3 at asecond time, t₂. An example of a current that is between the Threshold 2and the Threshold 3 is the current 852 in FIG. 8C. As shown in FIG. 8F,a current between the Threshold 2 and the Threshold 3 corresponds to acapacitance 864 (below the capacitance 866), e.g., due to the first setof narrow portions and the second set of narrow portions transitioningto the non-superconducting state as shown in FIG. 8C. The gate current870 transitions from below the Threshold 3 to above the Threshold 3 at athird time, t₃. An example of a current that is above the Threshold 3 isthe current 854 in FIG. 8D. As shown in FIG. 8F, a current above theThreshold 3 corresponds to a capacitance 862 (below the capacitance864), e.g., due to the first set of narrow portions, the second set ofnarrow portions, and the third set of narrow portions transitioning tothe non-superconducting state as shown in FIG. 8D. The gate current 870transitions from above the Threshold 3 to below the Threshold 3 at afourth time, t₄, which causes the superconducting circuit 800 totransition to a state in which the capacitance between the currentsource 308 and the readout circuit 710 of superconducting circuit 800 isthe second capacitance 864. The gate current 870 transitions from abovethe Threshold 2 to below the Threshold 2 at a fifth time, t₅, whichcauses the superconducting circuit 800 to transition to a state in whichthe capacitance between the current source 308 and the readout circuit710 of superconducting circuit 800 is the first capacitance 866.

FIGS. 9A-9B are schematic diagrams illustrating a superconductingcircuit 900 in an example programmed state (e.g., a selective inductor)in accordance with some embodiments. In FIG. 9A the narrow portions thatare shown in a cross-hatch pattern are in a non-superconducting state(e.g., a conductive or insulating state). In FIG. 9B the narrow portionsin the non-superconducting states are not shown. In some embodiments,the narrow portions are coupled to heat sources (e.g., heat sources 202as shown in FIGS. 2, 3, 4A, etc.); and the narrow portions in thenon-superconducting states are receiving heat from the correspondingheat sources. In some embodiments, the narrow portions are coupled tostrain sources (e.g., piezoelectric sources); and the narrow portions inthe non-superconducting states are receiving strain from thecorresponding strain sources. The non-superconducting narrow portionsresult in a relatively long path (as compared to other configurations ofthe thin film 702) from the current source 308 through the thin film 702to the readout circuit 710, resulting in relatively higher inductance(compared to other configurations of the thin film). In otherconfigurations of superconducting circuit 900, not shown, by changingwhich heat or strain sources are enabled and which are disabled, thepath from the current source 308 through the thin film 702 to thereadout circuit 710 is shorter than the path shown in FIG. 9B, resultingin lower inductance than the configuration shown in FIGS. 9A and 9B.Thus, the inductance of superconducting circuit 900 is selectable byselectively transitioning the narrow portions of superconducting circuit900 between superconducting and non-superconducting states.

FIG. 10A is a schematic diagram illustrating a superconducting circuit1000 in an example programmed state (e.g., a variable resistor) inaccordance with some embodiments. The superconducting circuit 1000includes a thin film 1002 having alternating wide portions and narrowportions. The thin film 1002 is coupled at a first terminal 1004 to acurrent source 308, and is coupled at a second terminal 1006 to areadout circuit 1010. Each narrow portion of the thin film 1002 iscoupled to a heat source 1012 (or optionally a piezoelectric source).The heat sources 1012 are coupled to a gate line via a set of resistors,e.g., resistors 1014, 1016, 1018, 1020, and 1022. The resistors1014-1022 have sequentially ascending resistance values such that theset of resistors operate as a current divider for currents received atthe gate line. In some embodiments, rather than coupling the heatsources to the current divider circuitry shown in FIG. 10A, eachindividual heat source is coupled to a distinct current source.

FIGS. 10B-10F are prophetic diagrams illustrating representativeoperating states of the superconducting circuit of FIG. 10A inaccordance with some embodiments. FIG. 10B shows a first current,current 1050, received at the gate line. FIG. 10B further shows thefirst heat source 1012-2 supplying sufficient heat to the correspondingnarrow portion 1003 to transition the narrow portion 1003 from thesuperconducting state to the non-superconducting state. The transitionof the first narrow portion results in a first resistance between thecurrent source 308 and the readout circuit 1010.

FIG. 10C shows a second current, current 1052, (e.g., greater than thecurrent 1050) received at the gate line. FIG. 10C further shows the heatsources 1012-2 and 1012-4 supplying sufficient heat to the correspondingnarrow portions 1003 and 1005 to transition those narrow portions fromthe superconducting state to the non-superconducting state. Thetransition of the narrow portions 1003 and 1005 results in a secondresistance (e.g., greater than the first resistance) between the currentsource 308 and the readout circuit 1010.

FIG. 10D shows a third current, current 1054, (e.g., greater than thecurrent 1052) received at the gate line. FIG. 10D further shows the heatsources 1012-2 through 1012-6 supplying sufficient heat to thecorresponding narrow portions 1003, 1005, and 1007 to transition thosenarrow portions from the superconducting state to thenon-superconducting state. The transition of the narrow portions 1003,1005, and 1007 results in a third resistance (e.g., greater than thesecond resistance) between the current source 308 and the readoutcircuit 1010.

FIG. 10E shows a fourth current, current 1056, (e.g., greater than thecurrent 1054) received at the gate line. FIG. 10E further shows the heatsources 1012-2 through 1012-8 supplying sufficient heat to thecorresponding narrow portions 1003, 1005, 1007, and 1009 to transitionthose narrow portions from the superconducting state to thenon-superconducting state. The transition of the narrow portions 1003,1005, 1007, and 1009 results in a fourth resistance (e.g., greater thanthe third resistance) between the current source 308 and the readoutcircuit 1010.

FIG. 10F shows a fifth current, current 1058, (e.g., greater than thecurrent 1056) received at the gate line. FIG. 10F further shows the heatsources 1012-2 through 1012-10 supplying sufficient heat to thecorresponding narrow portions 1003, 1005, 1007, 1009, and 1011 totransition those narrow portions from the superconducting state to thenon-superconducting state. The transition of the narrow portions 1003,1005, 1007, 1009, and 1011 results in a fifth resistance (e.g., greaterthan the fourth resistance) between the current source 308 and thereadout circuit 1010. Thus, FIGS. 10B-10F illustrate that thesuperconducting circuit 1000 operates as a variable resistor based on anamount of gate current supplied.

FIGS. 10G-10H are prophetic diagrams illustrating relationships betweengate current and resistance of the superconducting circuit of FIG. 10Ain accordance with some embodiments. FIG. 10G shows a gate current 1060changing over time. Specifically, the gate current 1060 transitions frombelow the Threshold 1 to above the Threshold 1 at a first time t₁. Anexample of a current that is between the Threshold 1 and the Threshold 2is the current 1050 in FIG. 10B. As shown in FIG. 10H, a current betweenthe Threshold 1 and the Threshold 2 corresponds to a first resistance1070, e.g., due to the first narrow portion transitioning to thenon-superconducting state as shown in FIG. 10B. The gate current 1060transitions from below the Threshold 2 to above the Threshold 3 at asecond time, t₂. An example of a current that is between the Threshold 2and the Threshold 3 is the current 1052 in FIG. 10C. As shown in FIG.10H, a current between the Threshold 2 and the Threshold 3 correspondsto a second resistance 1072 (above the resistance 1070), e.g., due tothe first and the second narrow portions transitioning to thenon-superconducting state as shown in FIG. 10C. The gate current 1060transitions from below the Threshold 3 to above the Threshold 3 at athird time, t₃. An example of a current that is between the Threshold 3and the Threshold 4 is the current 1054 in FIG. 10D. As shown in FIG.10H, a current between the Threshold 3 and Threshold 4 corresponds to athird resistance 1074 (above the resistance 1072), e.g., due to thefirst second, and third narrow portions transitioning to thenon-superconducting state as shown in FIG. 10D. The gate current 1060transitions from below the Threshold 4 to above the Threshold 4 at afourth time, t₄. An example of a current that is between the Threshold 4and the Threshold 5 is the current 1056 in FIG. 10E. As shown in FIG.10H, a current between the Threshold 4 and the Threshold 5 correspondsto a fourth resistance 1076 (above the resistance 1074), e.g., due tothe first second, third, and fourth narrow portions transitioning to thenon-superconducting state as shown in FIG. 10E. The gate current 1060transitions from below the Threshold 5 to above the Threshold 5 at afifth time, t₅. An example of a current that is above the Threshold 5 isthe current 1058 in FIG. 10F. As shown in FIG. 10H, a current above theThreshold 5 corresponds to a fifth resistance 1078 (above the resistance1076), e.g., due to the first second, third, fourth, and fifth narrowportions transitioning to the non-superconducting state as shown in FIG.10F. The gate current 1060 transitions from above the Threshold 5 tobelow the Threshold 5 at a sixth time, t₆, which causes thesuperconducting circuit 1000 to transition to a state in which theresistance between the current source 308 and the readout circuit 1010of superconducting circuit 1000 is the fourth resistance 1076. The gatecurrent 1060 transitions from above the Threshold 4 to below theThreshold 4 at a seventh time, t₇, which causes the superconductingcircuit 1000 to transition to a state in which the resistance betweenthe current source 308 and the readout circuit 1010 of superconductingcircuit 1000 is the third resistance 1074. The gate current 1060transitions from above the Threshold 3 to below the Threshold 3 at aneighth time, t₈, which causes the superconducting circuit 1000 totransition to a state in which the resistance between the current source308 and the readout circuit 1010 of superconducting circuit 1000 is thesecond resistance 1072. The gate current 1060 transitions from above theThreshold 2 to below the Threshold 2 at a ninth time, t₉, which causesthe superconducting circuit 1000 to transition to a state in which theresistance between the current source 308 and the readout circuit 1010of superconducting circuit 1000 is the first resistance 1070.

The above figures are described with respect to heat sources (e.g., heatsources 202). In some embodiments the heat sources are configured togenerate heat in response to a current source, such as a detectorcomponent that generates current in response to detecting photon(s). Insome embodiments, the heat sources are superconductor components thatgenerate heat while in a non-superconducting state. In some embodiments,the heat sources are resistive elements that generate heat as currentflows through them. In some embodiments, one or more of the heat sourcesis a thermal source configured to adjust a temperature of thecorresponding narrow portion to transition the narrow portion from thesuperconducting state to the non-superconducting state. In someembodiments, one or more of the heat sources is replaced by a strainsource (e.g., a piezoelectric source) configured to selectively apply astrain to the corresponding narrow portion sufficient to transition thenarrow portion from the superconducting state to the non-superconductingstate.

In light of these principles and embodiments, we now turn to certainadditional embodiments.

In accordance with some embodiments, a programmable circuit (e.g.,superconducting circuit 300, FIG. 3) includes: (1) a superconductingcomponent (e.g., thin film 201) arranged in a multi-dimensional array ofalternating narrow and wide portions, the superconducting componenthaving an input terminal at a first end (e.g., terminal 304) and anoutput terminal at a second end opposite of the first end (e.g.,terminal 302); and (2) control circuitry (e.g., heat sources 202)coupled to the narrow portions of the superconducting component, thecontrol circuitry configured to selectively transition the narrowportions between superconducting and non-superconducting states.

In some embodiments: (1) the control circuitry includes heat sources(e.g., heat source 202) coupled to respective narrow portions of thesuperconducting component; and (2) the control circuitry selectivelytransitions the narrow portions from the superconducting state to thenon-superconducting states by selectively providing heat via the heatsources (e.g., as illustrated in FIG. 6B).

In some embodiments: (A) the control circuitry further includes: (1) agate terminal (e.g., gate line, FIG. 8A); (2) a first resistor (e.g.,resistor 810) coupled between the gate terminal and a first set of heatsources, where the first set of heat sources are coupled to a first setof narrow portions of the superconducting component; and (3) a secondresistor (e.g., resistor 812) coupled between the gate terminal and asecond set of heat sources, where the second set of heat sources arecoupled to a second set of narrow portions of the superconductingcomponent, and where the second resistor has a higher resistance thanthe first resistor; and (B) where transition of the first set or thesecond set of narrow portions from the superconducting state to thenon-superconducting state prevents current flow from the input terminalto the output terminal (e.g., as illustrated in FIGS. 8B and 8C).

In some embodiments: (1) the programmable circuit further includes acurrent source coupled to the gate terminal of the control circuitry;(2) the current source is configured to selectively supply to thecontrol circuitry: (a) a first current (e.g., current 850, FIG. 8B)sufficient to transition the first set of narrow portions from thesuperconducting state to the non-superconducting state and insufficientto transition the second set of narrow portions from the superconductingstate to the non-superconducting state; and (b) a second current (e.g.,current 852, FIG. 8C) sufficient to transition the first and second setsof narrow portions from the superconducting state to thenon-superconducting state. Thus, in these embodiments the programmablecircuit operates the superconducting component as a variable capacitor.

In some embodiments, the control circuitry further includes: (1) agate-in terminal (e.g., gate line, FIG. 6A) coupled to a first heatsource (e.g., heat source 202-2), the first heat sourcethermally-coupled to a first narrow portion of the superconductingcomponent; (2) a bias terminal (e.g., bias line, FIG. 6A); (3) a firstresistor (e.g., resistor 610) coupled between the bias terminal and asecond heat source (e.g., heat source 202-7), the second heat sourcethermally-coupled to a second narrow portion of the superconductingcomponent; and (4) a second resistor (e.g., resistor 612) coupledbetween the bias terminal and a third heat source (e.g., heat source202-11), the third heat source thermally-coupled to a third narrowportion of the superconducting component, the second resistor having ahigher resistance than the first resistor.

In some embodiments: (A) the programmable circuit further includes: (1)a first current source coupled to the gate-in terminal; and (2) a biascurrent source coupled to the bias terminal; (B) the bias current sourceis configured to supply a bias current (e.g., bias current 619, FIG. 6B)insufficient, in the absence of current from the first current source,to transition the second narrow portion or the third narrow portion tothe non-superconducting state; and (C) the first current source isconfigured to selectively supply a first current (e.g., current 640,FIG. 6C), where the first current causes the first heat source to supplyheat to the first narrow portion, the heat sufficient to transition thefirst narrow portion from the superconducting state to thenon-superconducting state (e.g., as illustrated in FIG. 6C). In someembodiments, transition of the first narrow portion redirects currentflowing through the superconductor component to the other narrowportions. In some embodiments, the redirected current causes the othernarrow portions in the row to sequentially transition from thesuperconducting state to the non-superconducting state (e.g., asillustrated in FIGS. 6D-6F). In some embodiments, transition of all ofthe narrow portions in the row result in current being redirected to areadout circuit (e.g., readout circuit 608). In some embodiments, thecurrent flowing through the superconductor component initially and beingredirected to the readout circuit (e.g., current 620) exceeds thecurrent supplied to the gate terminal (e.g., current 640). Thus, inthese embodiments the programmable circuit operates the superconductingcomponent as a cascading current amplifier.

In some embodiments: (1) the control circuitry further includes: (A) agate-in terminal; (B) a first resistor coupled between the gate-interminal and a first heat source, the first heat sourcethermally-coupled to a first narrow portion of the superconductingcomponent; (C) a second resistor coupled between the gate-in terminaland a second heat source, the second heat source thermally-coupled to asecond narrow portion of the superconducting component, the secondresistor having a higher resistance than the first resistor; and (D) athird resistor coupled between the gate-in terminal and a third heatsource, the third heat source thermally-coupled to a third narrowportion of the superconducting component, the third resistor having ahigher resistance than the second resistor.

In some embodiments, the programmable circuit further includes a firstcurrent source coupled to the gate-in terminal (e.g., the gate line,FIG. 10A) and configured to selectively supply to the control circuitry:(a) a first current (e.g., current 1050, FIG. 10B) sufficient totransition the first narrow portion from the superconducting state tothe non-superconducting state and insufficient to transition the secondand third portions from the superconducting state to thenon-superconducting state; (b) a second current (e.g., current 1052,FIG. 10C) sufficient to transition the first and second narrow portionsfrom the superconducting state to the non-superconducting state andinsufficient to transition the third portion from the superconductingstate to the non-superconducting state; and (c) a third current (e.g.,current 1054, FIG. 10D) sufficient to transition the first, second, andthird narrow portions from the superconducting state to thenon-superconducting state. Thus, in these embodiments the programmablecircuit may operate the superconducting component as ananalog-to-digital converter (ADC) or a potentiometer.

In some embodiments, the control circuitry includes piezoelectricsources coupled to respective narrow portions of the superconductingcomponent; and the control circuitry transitions the narrow portionsfrom the superconducting state to the non-superconducting states byselectively providing mechanical-strain via the piezoelectric sources.

In accordance with some embodiments, a programmable circuit (e.g.,superconducting circuit 400, FIG. 4A) includes: (1) a configurablesuperconducting component (e.g., thin film 201) having an input terminal(e.g., terminal 304), an output terminal (e.g., terminal 302), and aplurality of gate terminals (e.g., for each narrow portion of the thinfilm 201); and (2) control circuitry (e.g., heat sources 202) coupled tothe superconducting component via the plurality of gate terminals, thecontrol circuitry adapted to selectively adjust capacitance, inductance,and/or resistance of the superconducting component. In some embodiments,the superconducting component includes a multi-dimensional array ofalternating narrow and wide portions; and the gate terminals correspondto respective narrow portions of the superconducting component. In someembodiments, activating a gate terminal includes transitioning thenarrow portion from a superconducting state to a non-superconductingstate (e.g., as described above with respect to FIG. 4A).

In some embodiments, the control circuitry is configured to concurrentlyactivate a subset of the plurality of gate terminals so as to inhibitcurrent flow from the input terminal to the output terminal (e.g., asillustrated in FIGS. 4A-4B). Thus, in these embodiments the programmablecircuit operates the superconducting component as a capacitor.

In some embodiments, the control circuitry is configured to selectivelyactivate distinct subsets of the plurality of gate terminals to adjust acapacitance of the superconducting component (e.g., as illustrated inFIGS. 6A-6F).

In some embodiments, the control circuitry is configured to concurrentlyactivate a subset of the plurality of gate terminals so as to increase apath length for current flowing from the input terminal to the outputterminal (e.g., as illustrated in FIGS. 9A-9B). Thus, in theseembodiments the programmable circuit operates the superconductingcomponent as an inductor. In some embodiments, the control circuitry isconfigured to selectively activate distinct subsets of the plurality ofgate terminals to adjust an inductance of the superconducting component.

In some embodiments, the control circuitry is thermally-coupled to, andelectrically-insulated from, the plurality of gate terminals (e.g., asdescribed above with respect to heat sources 202).

In some embodiments, the programmable circuit further includes a currentsource (e.g., the current source 308, FIG. 3) coupled to the inputterminal of the superconducting component, the current source adapted tosupply a bias current to the superconducting component. In someembodiments, the bias current is adapted to maintain the superconductingcomponent in a superconducting state in the absence of activation of anyof the gate terminals. In some embodiments, the programmable circuitfurther includes an output component (e.g., the readout circuit 306,FIG. 3) coupled to the output terminal of the superconducting component.

Although some of various drawings illustrate a number of logical stagesin a particular order, stages that are not order dependent may bereordered and other stages may be combined or broken out. While somereordering or other groupings are specifically mentioned, others will beobvious to those of ordinary skill in the art, so the ordering andgroupings presented herein are not an exhaustive list of alternatives.Moreover, it should be recognized that the stages could be implementedin hardware, firmware, software or any combination thereof.

It will also be understood that, although the terms first, second, etc.are, in some instances, used herein to describe various elements, theseelements should not be limited by these terms. These terms are only usedto distinguish one element from another. For example, a first currentcould be termed a second current, and, similarly, a second current couldbe termed a first current, without departing from the scope of thevarious described embodiments. The first current and the second currentare both currents, but they are not the same condition unless explicitlystated as such.

The terminology used in the description of the various describedembodiments herein is for the purpose of describing particularembodiments only and is not intended to be limiting. As used in thedescription of the various described embodiments and the appendedclaims, the singular forms “a”, “an” and “the” are intended to includethe plural forms as well, unless the context clearly indicatesotherwise. It will also be understood that the term “and/or” as usedherein refers to and encompasses any and all possible combinations ofone or more of the associated listed items. It will be furtherunderstood that the terms “includes,” “including,” “comprises,” and/or“comprising,” when used in this specification, specify the presence ofstated features, integers, steps, operations, elements, and/orcomponents, but do not preclude the presence or addition of one or moreother features, integers, steps, operations, elements, components,and/or groups thereof.

As used herein, the term “if” is, optionally, construed to mean “when”or “upon” or “in response to determining” or “in response to detecting”or “in accordance with a determination that,” depending on the context.Similarly, the phrase “if it is determined” or “if [a stated conditionor event] is detected” is, optionally, construed to mean “upondetermining” or “in response to determining” or “upon detecting [thestated condition or event]” or “in response to detecting [the statedcondition or event]” or “in accordance with a determination that [astated condition or event] is detected,” depending on the context.

The foregoing description, for purpose of explanation, has beendescribed with reference to specific embodiments. However, theillustrative discussions above are not intended to be exhaustive or tolimit the scope of the claims to the precise forms disclosed. Manymodifications and variations are possible in view of the aboveteachings. The embodiments were chosen in order to best explain theprinciples underlying the claims and their practical applications, tothereby enable others skilled in the art to best use the embodimentswith various modifications as are suited to the particular usescontemplated.

What is claimed is:
 1. A programmable circuit, comprising: asuperconducting component arranged in a multi-dimensional array ofalternating narrow and wide portions, the superconducting componenthaving an input terminal at a first end and an output terminal at asecond end opposite of the first end; and control circuitry coupled tothe narrow portions of the superconducting component, the controlcircuitry configured to selectively transition the narrow portionsbetween superconducting and non-superconducting states, wherein: thecontrol circuitry includes: heat sources coupled to respective narrowportions of the superconducting component; a gate terminal; a firstresistor coupled between the gate terminal and a first set of heatsources, wherein the first set of heat sources are coupled to a firstset of narrow portions of the superconducting component; and a secondresistor coupled between the gate terminal and a second set of heatsources, wherein the second set of heat sources are coupled to a secondset of narrow portions of the superconducting component, and the secondresistor has a higher resistance than the first resistor; wherein thecontrol circuitry selectively transitions the narrow portions from thesuperconducting state to the non-superconducting state by selectivelyproviding heat via the heat sources; and wherein transition of the firstset or the second set of narrow portions from the superconducting stateto the non-superconducting state prevents current flow from the inputterminal to the output terminal.
 2. The programmable circuit of claim 1,further comprising a current source coupled to the gate terminal of thecontrol circuitry; wherein the current source is configured toselectively supply to the control circuitry: a first current sufficientto transition the first set of narrow portions from the superconductingstate to the non-superconducting state and insufficient to transitionthe second set of narrow portions from the superconducting state to thenon-superconducting state; and a second current sufficient to transitionthe first and second sets of narrow portions from the superconductingstate to the non-superconducting state.
 3. The programmable circuit ofclaim 1, wherein the control circuitry further comprises: a gate-interminal coupled to a first heat source, the first heat sourcethermally-coupled to a first narrow portion of the superconductingcomponent; a bias terminal; a first bias resistor coupled between thebias terminal and a second heat source, the second heat sourcethermally-coupled to a second narrow portion of the superconductingcomponent; and a second bias resistor coupled between the bias terminaland a third heat source, the third heat source thermally-coupled to athird narrow portion of the superconducting component, the secondresistor having a higher resistance than the first resistor.
 4. Theprogrammable circuit of claim 3, further comprising: a first currentsource coupled to the gate-in terminal; and a bias current sourcecoupled to the bias terminal; wherein the bias current source isconfigured to supply a bias current insufficient, in the absence ofcurrent from the first current source, to transition the second narrowportion or the third narrow portion to the non-superconducting state;and wherein the first current source is configured to selectively supplya first current, wherein the first current causes the first heat sourceto supply heat to the first narrow portion, the heat sufficient totransition the first narrow portion from the superconducting state tothe non-superconducting state.
 5. The programmable circuit of claim 1,wherein the control circuitry comprises piezoelectric sources coupled torespective narrow portions of the superconducting component; and whereinthe control circuitry selectively transitions the narrow portions fromthe superconducting state to the non-superconducting states byselectively providing mechanical-strain via the piezoelectric sources.6. A programmable circuit, comprising: a superconducting componentarranged in a multi-dimensional array of alternating narrow and wideportions, the superconducting component having an input terminal at afirst end and an output terminal at a second end opposite of the firstend; and control circuitry coupled to the narrow portions of thesuperconducting component, the control circuitry configured toselectively transition the narrow portions between superconducting andnon-superconducting states, wherein: the control circuitry comprisesheat sources coupled to respective narrow portions of thesuperconducting component; the control circuitry selectively transitionsthe narrow portions from the superconducting state to thenon-superconducting states by selectively providing heat via the heatsources; and the control circuitry further comprises: a gate-interminal; a first resistor coupled between the gate-in terminal and afirst heat source, the first heat source thermally-coupled to a firstnarrow portion of the superconducting component; a second resistorcoupled between the gate-in terminal and a second heat source, thesecond heat source thermally-coupled to a second narrow portion of thesuperconducting component, the second resistor having a higherresistance than the first resistor; and a third resistor coupled betweenthe gate-in terminal and a third heat source, the third heat sourcethermally-coupled to a third narrow portion of the superconductingcomponent, the third resistor having a higher resistance than the secondresistor.
 7. The programmable circuit of claim 6, further comprising: afirst current source coupled to the gate-in terminal and configured toselectively supply to the control circuitry: a first current sufficientto transition the first narrow portion from the superconducting state tothe non-superconducting state and insufficient to transition the secondand third narrow portions from the superconducting state to thenon-superconducting state; a second current sufficient to transition thefirst and second narrow portions from the superconducting state to thenon-superconducting state and insufficient to transition the thirdnarrow portion from the superconducting state to the non-superconductingstate; and a third current sufficient to transition the first, second,and third narrow portions from the superconducting state to thenon-superconducting state.
 8. A programmable circuit, comprising: aconfigurable superconducting component having an input terminal, anoutput terminal, and a plurality of gate terminals; and controlcircuitry coupled to the configurable superconducting component via theplurality of gate terminals, the control circuitry adapted toselectively adjust capacitance, inductance, or resistance of theconfigurable superconducting component, wherein: the control circuitryincludes: heat sources coupled to gate terminals of the plurality ofgate terminals: a gate-in terminal; a first resistor coupled between thegate-in terminal and a first set of heat sources, wherein the first setof heat sources are coupled to a first set of gate terminals of theplurality of gate terminals; and a second resistor coupled between thegate-in terminal and a second set of heat sources, wherein the secondset of heat sources are coupled to a second set of gate terminals of theplurality of gate terminals, and the second resistor has a higherresistance than the first resistor; wherein the control circuitryselectively transitions the gate terminals from a superconducting stateto a non-superconducting state by selectively providing heat via theheat sources; and wherein transition of the first set or the second setof gate terminals from the superconducting state to thenon-superconducting state prevents current flow from the input terminalto the output terminal.
 9. The programmable circuit of claim 8, whereinthe configurable superconducting component comprises a multi-dimensionalarray of alternating narrow and wide portions; and wherein the gateterminals correspond to respective narrow portions of the configurablesuperconducting component.
 10. The programmable circuit of claim 9,wherein the control circuitry is configured to concurrently activate asubset of the plurality of gate terminals so as to inhibit current flowfrom the input terminal to the output terminal.
 11. The programmablecircuit of claim 10, wherein the control circuitry is configured toselectively activate distinct subsets of the plurality of gate terminalsto adjust a capacitance of the configurable superconducting component.12. The programmable circuit of claim 9, wherein the control circuitryis configured to concurrently activate a subset of the plurality of gateterminals so as to increase a path length for current flowing from theinput terminal to the output terminal.
 13. The programmable circuit ofclaim 12, wherein the control circuitry is configured to selectivelyactivate distinct subsets of the plurality of gate terminals to adjustan inductance of the configurable superconducting component.
 14. Theprogrammable circuit of claim 8, wherein the control circuitry isthermally-coupled to, and electrically-insulated from, the plurality ofgate terminals.
 15. The programmable circuit of claim 8, furthercomprising a current source coupled to the input terminal of theconfigurable superconducting component, the current source adapted tosupply a bias current to the configurable superconducting component. 16.The programmable circuit of claim 8, further comprising an outputcomponent coupled to the output terminal of the configurablesuperconducting component.